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arXiv:2001.11946

A hybrid quantum enabled RBM advantage: convolutional autoencoders for quantum image compression and generative learning

Jennifer Sleeman, John E. Dorband, Milton Halem

Published Apr 24, 2020• 26 citations
arXivHTMLPDF

Abstract

Understanding how the D-Wave quantum computer could be used for machine learning problems is of growing interest. Our work explores the feasibility of using the D-Wave as a sampler for a machine learning task. We describe a hybrid method that combines a classical deep neural network autoencoder with a quantum annealing Restricted Boltzmann Machine (RBM) using the D-Wave for image generation. Our method overcomes two key limitations in the 2000-qubit D-Wave processor, namely the limited number of qubits available to accommodate typical problem sizes for fully connected quantum objective functions, and samples that are binary pixel representations. As a consequence of these limitations we are able to show how we achieved nearly a 22-fold compression factor of grayscale 28 x 28 sized images to binary 6 x 6 sized images with a lossy recovery of the original 28 x 28 grayscale images. We further show how generating samples from the D-Wave after training the RBM, resulted in 28 x 28 images that were variations of the original input data distribution, as opposed to recreating the training samples. We evaluated the quality of this method by using a downstream classification method. We formulated a MNIST classification problem using a deep convolutional neural network that used samples from the quantum RBM to train the MNIST classifier and compared the results with a MNIST classifier trained with the original MNIST training data set, as well as a MNIST classifier trained using classical RBM samples. We also explored using a secondary dataset, the MNIST Fashion dataset and demonstrate the first quantum-generated fashion. Our hybrid autoencoder approach indicates advantage for RBM results relative to the use of a current RBM classical computer implementation for image-based machine learning and even more promising results for the next generation D-Wave quantum system. Our method for compression and image mappings is not constrained to RBMs, the autoencoder part of this method could be coupled with other quantum-based algorithms.

DOI
10.1117/12.2558832

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Understanding how the D-Wave quantum computer could be used for machine learning problems is of growing interest. Our work explores the feasibility of using the D-Wave as a sampler for a machine learning task. We describe a hybrid method that combines a classical deep neural network autoencoder with a quantum annealing Restricted Boltzmann Machine (RBM) using the D-Wave for image generation. Our method overcomes two key limitations in the 2000-qubit D-Wave processor, namely the limited number of qubits available to accommodate typical problem sizes for fully connected quantum objective functions, and samples that are binary pixel representations. As a consequence of these limitations we are able to show how we achieved nearly a 22-fold compression factor of grayscale 28 x 28 sized images to binary 6 x 6 sized images with a lossy recovery of the original 28 x 28 grayscale images. We further show how generating samples from the D-Wave after training the RBM, resulted in 28 x 28 images that were variations of the original input data distribution, as opposed to recreating the training samples. We evaluated the quality of this method by using a downstream classification method. We formulated a MNIST classification problem using a deep convolutional neural network that used samples from the quantum RBM to train the MNIST classifier and compared the results with a MNIST classifier trained with the original MNIST training data set, as well as a MNIST classifier trained using classical RBM samples. We also explored using a secondary dataset, the MNIST Fashion dataset and demonstrate the first quantum-generated fashion. Our hybrid autoencoder approach indicates advantage for RBM results relative to the use of a current RBM classical computer implementation for image-based machine learning and even more promising results for the next generation D-Wave quantum system. Our method for compression and image mappings is not constrained to RBMs, the autoencoder part of this method could be coupled with other quantum-based algorithms.
Computer vision has a wide range of applications from medical image analysis to robotics. Over the past few years, the field has been transformed by machine learning and stands to benefit from potential advances in quantum computing. The main challenge for processing images on current and near-term quantum devices is the size of the data such devices can process. Images can be large, multidimensional and have multiple color channels. Current machine learning approaches to computer vision that exploit quantum resources require a significant amount of manual pre-processing of the images in order to be able to fit them onto the device. This paper proposes a framework to address the problem of processing large scale data on small quantum devices. This framework does not require any dataset-specific processing or information and works on large, grayscale and RGB images. Furthermore, it is capable of scaling to larger quantum hardware architectures as they become available. In the proposed approach, a classical autoencoder is trained to compress the image data to a size that can be loaded onto a quantum device. Then, a Restricted Boltzmann Machine (RBM) is trained on the D-Wave device using the compressed data, and the weights from the RBM are then used to initialize a neural network for image classification. Results are demonstrated on two MNIST datasets and two medical imaging datasets.
The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to, and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from either a quantum or classical Boltzmann machine (QBM or BM). This setup allows quantum-assisted training of deep generative models by physically simulating the generative process with quantum annealers. In this paper, we have successfully employed D-Wave quantum annealers as Boltzmann samplers to perform quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE allows us to deploy current-generation quantum annealers in QCH generative models to achieve competitive performance on datasets such as MNIST. The results presented in this paper suggest that commercially available quantum annealers can be deployed, in conjunction with well-crafted classical deep neutral networks, to achieve competitive results in unsupervised and semisupervised tasks on large-scale datasets. We also provide evidence that our setup is able to exploit large latent-space (Q)BMs, which develop slowly mixing modes. This expressive latent space results in slow and inefficient classical sampling, and paves the way to achieve quantum advantage with quantum annealing in realistic sampling applications.
The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in reference [ 1 ] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from a quantum Boltzmann machine (QBM). This setup allows quantum-assisted training of deep generative models by physically simulating the generative process with quantum annealers. In this paper, we have successfully employed D-Wave quantum annealers as Boltzmann samplers to perform quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE allows us to deploy current-generation quantum annealers in QCH generative models to achieve competitive performance on datasets such as MNIST. The results presented in this paper suggest that commercially available quantum annealers can be deployed, in conjunction with well-crafted classical deep neutral networks, to achieve competitive results in unsupervised and semisupervised tasks on large-scale datasets. We also provide evidence that our setup is able to exploit large latent-space QBMs, which develop slowly mixing modes. This expressive latent space results in slow and inefficient classical sampling and paves the way to achieve quantum advantage with quantum annealing in realistic sampling applications.
Restricted Boltzmann Machines trained by the classical Contrastive Divergence algorithm were embedded into a next generation D-Wave quantum computer having more than 2000 qubits. The embedding was used to sample missing visible units and labels of incomplete test images. The previously introduced RBM embedding that combined qubits into individual RBM units in order to increase the connectivity between units was used. In comparison to the 1000 qubit machine investigated earlier, the same embedding approach applied to the 2000 qubit D-Wave enabled a connectivity between RBM units sufficient for RBM training on a classical computer with a satisfactory classification error. After a varied number of CD training iterations, the visible units corresponding to a particular incomplete test image were fixed in the D-Wave embedding. The resulting state returned by the D-Wave represents the most energetically favorable combination of the remaining qubits for the given fixed incomplete input image. The classification errors compared favorably to those obtained by the classical MCMC sampling. Main factors influencing the quality of the embedding were investigated. Regardless of the computational cost incentives for using the D-Wave for this operation, the reconstruction and classification errors determined in this way can be used at least as a verification of the validity and quality of the particular embedding of the given RBM architecture. This is essential for successfully employing a QC in much more computationally demanding parts of the RBM training. opportunities for using QC not only for recognition but especially for RBM training, in particular for obtaining a representative sample from the RBM model distribution, are discussed.
Abstract Classification and data reconstruction using a restricted Boltzmann machine (RBM) is presented. RBM is an energy-based model which assigns low energy values to the configurations of interest. It is a generative model, once trained it can be used to produce samples from the target distribution. The D-Wave 2000Q is a quantum computer which has been used to exploit its quantum effect for machine learning. Bars-and-stripes (BAS) and cybersecurity (ISCX) datasets were used to train RBMs. The weights and biases of trained RBMs were used to map onto the D-Wave. Classification as well as image reconstruction were performed. Classification accuracy of both datasets indicates comparable performance using D-Wave’s adiabatic annealing and classical Gibb’s sampling.